[geometry-ml:01511] 第 7 回阪大 - 阪市大‐神戸大 - 九大合同幾何学セミナー (GEOSOCKseminar)

[ohnita]

皆様

阪大-阪市大‐神戸大-九大合同幾何学セミナー
GEOSOCK seminar (GEO=geometry, OS=Osaka University, OC=Osaka City
University,
K=Kobe University&Kyushu University)

の第7回を以下の要領で開催しますので、ご案内申し上げます。
ご関心のある方々のご参加を大いに期待しております。

開催日： 平成２４年７月２８日（土）１０：００〜１７：００
場所：大阪市立大学（杉本キャンバス）　理学部棟3階　３０４０室（数学講究室）

プログラム：

Mason Pember (University of Bath, UK & Kobe University)
10:00-11:00 "Lie Sphere Geometry"
Abstract:　
We will give a basic introduction to Lie sphere geometry, the study of
oriented spheres
and their oriented contact in 3-dimensional Riemannian and Lorentzian
space forms.
We will see how this can be used to study the differential geometry of
surfaces, and
more generally fronts, in these space forms. For simplicity's sake, we
will mainly focus
on S^3.

David Brander教授 集中講義
「曲面論におけるDPW型手法」 "DPW-type Methods in Surface Theory"
11:30-12:30 : Lecture (I)
14:30-15:30 : Lecture (II)　
16:00-15:30 : Lecture (III)
Abstract:　
Over the last 20 years loop group methods have been used
to study many "classical" classes of surfaces in space forms; for
example, constant mean or Gauss curvature surfaces. These types of
surfaces are sometimes called "integrable surfaces", and the
relevant property is that the surfaces are characterized by the
existence of a special type of map (which is easy to describe)
into a subgroup of the group of loops in a complex semisimple
Lie group. There are at least three different basic ideas which
can be used to generate solutions: dressing, the AKS-type theory
for finite type solutions, and the "DPW"-type method.

In these talks I will describe the last mentioned of these. This
method has the property that it produces ALL solutions for the
problem at hand from simpler data, in analogue to the classical
Weierstrass representation for minimal surfaces. The challenge,
however, is that it is difficult to read geometric information
about the surface in the generalized Weierstrass data, due to a
loop group splitting involved in passing between the two
equivalent pieces of information. A basic idea which can be
exploited is that the Weierstrass data associated to a given
surface is not unique, and therefore one may try to choose this in
such a way as to make this issue easier. I will illustrate this
with two examples: one is the solution of the generalization of
Bjorling's problem to other surface classes; the other is the use
of special potentials to analyze singularities of surfaces.
These ideas can be implemented both for surfaces associated to
Riemannian harmonic maps, which have a generalized Weierstrass
representation in terms of holomorphic functions, and for those
associated to Lorentzian harmonic maps, which have a generalized
d'Alembert type solution.


組織者：後藤竜司（大阪大学）, Wayne Rossman（神戸大学）, 小磯深幸（九州
大学),
大仁田義裕（大阪市立大学）
主催：大阪大学大学院理学研究科、神戸大学大学院理学研究科、九州大学大学院
数理学研究院、大阪市立大学数学研究所

詳細は、下記ホームページをご参照ください。
URL ：
http://www.sci.osaka-cu.ac.jp/~ohnita/2012/GEOSOCKsem/GEOSOCKsem120728.html

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お問い合わせ（e-mail）
Wayne Rossman： wayne ＠ math.kobe-u.ac.jp
大仁田　義裕 ： ohnita ＠ sci.osaka-cu.ac.jp
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